Which of the following numbers is a multiple of 3? ${53,54,83,101,113}$
Explanation: The multiples of $3$ are $3$ $6$ $9$ $12$ ..... In general, any number that leaves no remainder when divided by $3$ is considered a multiple of $3$ We can start by dividing each of our answer choices by $3$ $53 \div 3 = 17\text{ R }2$ $54 \div 3 = 18$ $83 \div 3 = 27\text{ R }2$ $101 \div 3 = 33\text{ R }2$ $113 \div 3 = 37\text{ R }2$ The only answer choice that leaves no remainder after the division is $54$ $ 18$ $3$ $54$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $54$ $54 = 2\times3\times3\times3 3 = 3$ Therefore the only multiple of $3$ out of our choices is $54$. We can say that $54$ is divisible by $3$.